How do you prove that # sin^2(x/2) = (1-cos^2x)/(2(1+cosx)) #?

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Answer 1 · 2016-01-09T14:48:16

This is not a valid identity.

Working only with the right hand side:

#(1-cos^2x)/(2(1+cosx))#

Use the Pythagorean Identity in the numerator.

#=sin^2x/(2(1+cosx))#

Split apart the fraction.

#=(sinx/2)(sinx/(1+cosx))#

Use the tangent half angle identity.

#=1/2sinxtan(x/2)#

There is nothing you could do here to make this equal #sin^2(x/2)#.